Science a GoGo's Home Page Forums General Discussion Not-Quite-Science Forum Puzzles...

Thought I would start a thread to exercise minds. If you have any to add, then please do.

You awake inside a small transparent capsule sitting on the surface of Venus. From a small speaker you hear a voice that says, "We will leave you here either for a day or a year. If you choose to stay a day, we will give you $1 million. If you choose to stay a year, we will give you $2 million. Either way, you will have sufficient food and water. We will make sure the temperature is a constant 70 degrees Fahrenheit. We will also supply cable TV."

What is your choice and why?

Based on "A bird in the hand is worth two in the bush" I'd settle for the million. I wouldn't want to guarantee my sanity after a year of solitary in a plastic bubble, even with TV. Maybe if I had an computer with internet...

But why not go for the more money and LESS time, if you're worried about your sanity?

Boy, you got a good bar bet going here Blacknad!

LOL

~~SA

I'd take the day. After a year sitting in a bubble you'd have trouble moving once you got out. Mind you some people say I move very little as it is.

Thanks Blacknad, I'm getting a lot of good chuckles from this. I bursting, but don't want to spoil the fun. How long do you...?

Guess I'll just reiterate:
"...go for the more money (the $2M.) and LESS time, if you're worried about your sanity?

Make sense?
Let me know, if not.

~SA

OK, not bad Blacknad! I've changed my mind and decided to take the cyanide instead

I agree with you Samwick 100%.

Mike Kremer.

I'd go with the year, since a Venusian day is a little longer than a Venusian year.

Congrats Samwick, Mike & Soilguy. I'm impressed.

Choose to stay one year and win $2 million. Venus takes 243 Earth days to rotate on its axis, but it takes 225 Earth days to go around the sun. On Venus a day is longer than a year.

Blacknad.

Another...

If you balance a broom horizontally on your finger, so that your finger is exactly on the broom's center of gravity, mark that spot and then cut the broom in two, then you'll have a long and a short piece. The long piece is most of the handle and the short piece has the bristle end and a small part of the handle. Now what happens if you weigh both pieces?

A) The short piece will weigh more.
B) The long piece will weigh more.
C) Both will weigh the same.

Blacknad.

If you cut it at exactly the center of gravity, each piece will weigh the same. There has to be the same weight on both sides of the center of gravity in order for the broom to balance.

Are you certain?

Blacknad

I'll take a shot:

The long piece will weigh more.

The weight wasn't evenly distributed. The longer piece was counterbalanced by the short piece because the short piece had extra mass at the end (so it had more leverage).

Cool! I never woulda guessed!

Very good rede;; I was thinking along those lines (unequal dist. of mass, torque?), but I couldn't decide which way it'd go. Seems as if the bristle end would be heavier, but I couldn't come up with a reason....



Maybe I should try to come up with a puzzle involving -- shower curtains.
Maybe not....

~~Later

Whoops, I didn't read your post close enough.

Which is it?
"The long piece will weigh more."
or
"the short piece had extra mass at the end"

I'll agree with the short piece needs the extra mass to counter the leverage of the long piece.
So, the short piece weighs more?

~SA

Has anyone done the experiment?

Regarding the broom analogy, I have an excellent proxy; a tack hammer with a ~45" handle (which conveniently is divided into 3 screw-in segments, with the first screw located at the balance point). I was playing with it just a couple of days ago and marveled at how well it was made and how they probably designed it with the balance point at the end of that first segment.

~SA

Hey, I've got a puzzle for you.

For what could a tack hammer, with a 45" handle, possibly be useful? There are some clips along one side of the hammer.
~SA

2 - 0 to Samwick - Nice one.

A) The short piece weighs more!

This is due to the torque needed to hold the long piece up. It is the same reason a heavy kid has to sit closer in on a see-saw when he is on it with a lighter friend.

See here for a complete explanation:

http://www.physicsforums.com/archive/index.php/t-47208.html

Blacknad.

Now for probability.

You are sentenced to death by the Emperor. He offers you a chance to live by playing a fun game. He gives you 50 black beads, 50 white beads and 2 empty bowls. He then says, "Divide these 100 beads into these 2 bowls. You can divide them any way you like as long as you use all the beads. Then I will blind you (there had to be a snag somewhere) and mix the bowls around. You then can choose one bowl and remove ONE bead. If the bead is WHITE you will live, but if the bead is BLACK... you will die horribly and painfully."

How do you divide the beads up so that you have the greatest probability of choosing a WHITE bead?

This is a good one with a very cool solution. Don't let Samwick increase his lead

Blacknad.

After being blinded, can we shake the bowls before choosing, or do we have to just blindly put a hand in a bowl and pick a bead?

If we can shake the bowls first, I'd put one white one in a bowl, and put the rest in the other.

No, the Emperor is cruel, not retarded.

Blacknad.

So, dividing the beads unequally won't work?

What about layering them? My first thought was to put white on top, but depending on the shape of the bowl....

For a wide bowl, I think it'd be best to put the white at the bottom and dig thru the black beads to pick a white bead (hopefully) off the bottom.

[edit]: Better yet, put the white in a mound in the center and put black ones around the perimeter (still digging down in the center to optimize white choice).[]

~SA

btw: the hammer weighed 24oz. & the handle extension was 20oz.

...or, depending on the size of the beads and bowl, maybe arrange a perimeter of white beads to choose from.

??
~samwik

Crush the black beads into dust.
Divide them however you wish so long as there is at least one white bead in each bowl.

I never said that

What division of beads gives you the greatest chance of survival?

There are some creative solutions here but the answer is a straightforward matter of probability.

Blacknad.

I'd leave the beads seperated into black and white bowls. Then I'd leave the bowls in the sun, in the hopes that the black ones will feel warmer than the white ones.

If that didn't work, then I'd take the bead dust that samwik created and fling it into the emperor's eyes. In the ensuing confusion, I'd grab some drapes or a tapestry, and swing Tarzan style, to safety.

Soilguy,

One point for trying and another for causing me to laugh out loud.

Blacknad.

Yes soilguy, I laughed out loud too (as ~nad says), and several times during the day! But I'm not the one who suggested crushing the beads up.

So does the emperor handle the bowls after we divide up the beads? Can the emperor shake the bowls?

I'm gonna go reread the original....

~Later

Actually, if you took 49 white beads and mixed them in with the black ones, leaving one white bead in a bowl, your probability of selecting a black bead drops to 0.2525, with a 0.7475 probability of selecting a white one.

P(W) = 0.5 + 0.5(0.49)

This is the probability of choosing the "white bowl" plus the probability of choosing a white bead if you were unfortunate enough to choose the "black bowl."

P(B) = 0.5(0.51)

This is the probability that you'd choose the "black bowl" and a black bead.

I was going to suggest the same solution as soilguy, but it looks like he beat me to it. One white bead in one bowl, and mix all the rest in the other bowl.

Soilguy,

First class answer. You had it at the top of page 3, but I wanted you to articulate it. Excellent.

Overdriven, welcome to SAGG - and I'll take your word for it

Blacknad.